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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2509.26459 |
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| _version_ | 1866915525574000640 |
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| author | Jaitly, Akshay Jha, Devesh K. Ota, Kei Shirai, Yuki |
| author_facet | Jaitly, Akshay Jha, Devesh K. Ota, Kei Shirai, Yuki |
| contents | Optimization-based methods are widely used for computing fast, diverse solutions for complex tasks such as collision-free movement or planning in the presence of contacts. However, most of these methods require enforcing non-penetration constraints between objects, resulting in a non-trivial and computationally expensive problem. This makes the use of optimization-based methods for planning and control challenging. In this paper, we present a method to efficiently enforce non-penetration of sets while performing optimization over their configuration, which is directly applicable to problems like collision-aware trajectory optimization. We introduce novel differentiable conditions with analytic expressions to achieve this. To enforce non-collision between non-smooth bodies using these conditions, we introduce a method to approximate polytopes as smooth semi-algebraic sets. We present several numerical experiments to demonstrate the performance of the proposed method and compare the performance with other baseline methods recently proposed in the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_26459 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Analytic Conditions for Differentiable Collision Detection in Trajectory Optimization Jaitly, Akshay Jha, Devesh K. Ota, Kei Shirai, Yuki Robotics Computational Geometry Optimization-based methods are widely used for computing fast, diverse solutions for complex tasks such as collision-free movement or planning in the presence of contacts. However, most of these methods require enforcing non-penetration constraints between objects, resulting in a non-trivial and computationally expensive problem. This makes the use of optimization-based methods for planning and control challenging. In this paper, we present a method to efficiently enforce non-penetration of sets while performing optimization over their configuration, which is directly applicable to problems like collision-aware trajectory optimization. We introduce novel differentiable conditions with analytic expressions to achieve this. To enforce non-collision between non-smooth bodies using these conditions, we introduce a method to approximate polytopes as smooth semi-algebraic sets. We present several numerical experiments to demonstrate the performance of the proposed method and compare the performance with other baseline methods recently proposed in the literature. |
| title | Analytic Conditions for Differentiable Collision Detection in Trajectory Optimization |
| topic | Robotics Computational Geometry |
| url | https://arxiv.org/abs/2509.26459 |